60.1.62 problem 62

Internal problem ID [10076]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 62
Date solved : Tuesday, January 28, 2025 at 04:24:43 PM
CAS classification : [NONE]

\begin{align*} y^{\prime }-\frac {y-x^{2} \sqrt {x^{2}-y^{2}}}{x y \sqrt {x^{2}-y^{2}}+x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 34

dsolve(diff(y(x),x) - (y(x)-x^2*sqrt(x^2-y(x)^2))/(x*y(x)*sqrt(x^2-y(x)^2)+x)=0,y(x), singsol=all)
 

\[ \frac {y^{2}}{2}+\arctan \left (\frac {y}{\sqrt {x^{2}-y^{2}}}\right )+\frac {x^{2}}{2}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 1.598 (sec). Leaf size: 44

DSolve[D[y[x],x] - (y[x]-x^2*Sqrt[x^2-y[x]^2])/(x*y[x]*Sqrt[x^2-y[x]^2]+x)==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-\arctan \left (\frac {\sqrt {x^2-y(x)^2}}{y(x)}\right )+\frac {x^2}{2}+\frac {y(x)^2}{2}=c_1,y(x)\right ] \]